Repair Café Capacity
A volunteer repair café in Limerick opens one Saturday a month from 10:00 to 13:00, staffed by three repairers who work in parallel. An item is handled by one repairer at a time, and repairs run back-to-back with no gaps. Twelve months of records show that 80% of items take 25 minutes and 20% take 50 minutes, with no other durations. Bookings are taken in advance, and the March session is already full at 30 items. The funder's conditions are that no booked item may be turned away on the day, and that the hall must be vacated by 13:00 sharp. Two repairers have offered to arrive at 09:00 to start early, but the hall key is not released before 10:00. The coordinator's note reads: '3 repairers × 3 hours = 540 minutes; at roughly 30 minutes an item that is 18 items, so we are 12 over - we will just work faster.'
1. Check the coordinator's capacity arithmetic and assess whether 'working faster' can close the gap.
Read the worked answer
The arithmetic is right. Available capacity = 3 repairers × 180 minutes = 540 repair-minutes. Expected time per item = 0.8 × 25 + 0.2 × 50 = 20 + 10 = 30 minutes. Expected capacity = 540 ÷ 30 = 18 items. With 30 booked, the expected shortfall is 12 items, or 12 × 30 = 360 repair-minutes - 120 extra minutes per repairer, i.e. the session would need to run to 15:00.
'Working faster' cannot close it. Even in the impossible case where all 30 items were the 25-minute type, the load would be 30 × 25 = 750 repair-minutes against 540 - still 210 minutes short, and that is the optimistic bound. Any realistic speed-up also trades against quality and safety on electrical and bike repairs, which is exactly the risk a volunteer café cannot take.
The more serious error is conceptual: the note treats the 30-minute figure as a target to beat rather than a description of the workload, so it draws no distinction between 'we have a plan to work faster' and 'we have 12 items with nowhere to go'.
2. Give three options that would make the March session compliant, with the numbers for each, and identify which option the funder's conditions actually permit.
Read the worked answer
1. Move bookings, not people. The funder's rule bars turning away a booked item on the day; it does not bar rebooking in advance. Moving 12 items to April, by phone this week and with an apology, satisfies the letter of the condition and keeps 18, exactly expected capacity.
2. Add repairers. Capacity scales linearly: 4 repairers give 4 × 180 = 720 minutes = 24 items; 5 repairers give 900 minutes = 30 items, but with zero expected slack - by the definition of an expectation, roughly half of such sessions run over. To cover 30 items with a workable margin you would want 6 repairers (1,080 minutes ÷ 30 = 36 items' worth, a 20% buffer).
3. Restructure the work. Pre-diagnose by photo or phone, so the 50-minute jobs are identified before the day and either given double slots or referred on; run a separate 'quick table' for jobs known to take under 15 minutes (fuse changes, cable adjustments, glue-ups) staffed by a fourth volunteer; have parts ordered in advance so no repairer waits on a supplier.
The early arrival at 09:00 is not an option at all - the key is not released before 10:00, so those two hours are unusable and should be struck from the coordinator's thinking.
3. The coordinator prefers to keep all 30 bookings and recruit a fifth repairer. Assess that plan and say what should be monitored.
Read the worked answer
It is arithmetically borderline and fragile. Five repairers provide 900 repair-minutes, which is exactly the expected load of 30 items at 30 minutes each. Matching expected load to capacity means a shortfall in about half of sessions, because the load varies: the worst case, 30 long jobs, is 30 × 50 = 1,500 minutes, 600 minutes beyond capacity. Even a modest run of long jobs - say 12 instead of the expected 6 - adds 6 × 25 = 150 minutes, enough to overrun by nearly an hour.
The plan also depends on volunteers who have not yet been recruited, and the funder's condition makes failure public: an overrun means either a booked item abandoned or the hall kept past 13:00, and both breach the agreement. The 09:00 offer does not help, because the hall is locked.
Safer version of the same instinct: recruit six, keep 30 bookings, and treat the sixth as the buffer; or recruit five and cap March at 24 items, rebooking 6 rather than 12.
What to monitor: actual repair durations by job type (to replace the 80/20 split with real data), the no-show rate (each no-show frees 30 minutes), overruns past 13:00, and the number of items rebooked. Review after the April session and set the booking cap from the observed distribution, not from the nominal average - the average is precisely what hides the risk.